[From the Introduction]

Over fifty years ago, C. S. Smith and C. Zener proposed that for grain growth in a random dispersion of rigid, immobile particles of radius r, the maximum attainable grain size R is given by R = a r/fb where f is the volume fraction of particles and a and b are constants [1]. Under the Smith-Zener assumptions, a = 4/3 and b = 1.

A number of subsequent investigators have proposed corrections to the Smith-Zener approach [2-10]. While these corrections modify a and b, a remains of order unity and b remains near one.
However, controversy about the validity of the Smith-Zener equation has continued for two reasons. First, experiments often do not find b = 1 [9,11]. Second, in the 1980s, computer simulations of particle pinned grain growth in three dimensions found b = 1/3 [12-14].

The inconsistency in experimental results is due to a variety of deficiencies in experimental design, including initial grain size larger than the predicted pinned size, particles which move or coarsen, solute or liquid present on the grain boundaries, and mechanical driving force for coarsening. A discussion of these issues is found in [15-18].

By examining the structures formed at particle/boundary intersections, Miodownik et al. found that previous Monte Carlo Potts model computer simulations of particle pinning were flawed as well [19]. Prior simulations were performed under thermodynamic conditions where particles can induce artificial facetting of grain boundaries along simulation lattice planes. This facetting removes boundary curvature and ultimately stops grain growth. When sufficient thermal energy is imparted to the system, the boundaries roughen, facets disappear, and the particle/boundary structure takes on the catenoid geometry predicted by Smith and Zener. Under these conditions, simulations of boundary motion in an idealized grain structure indicate a pinning exponent b ∼ 1, in agreement with the Smith-Zener theory [20].

While the idealized geometry examined by Miodownik et al. does not include the full topological complexity of a real grain microstructure, computational limitations have prevented pinning simulations on polycrystals. In this paper, we present the first results of correct particle pinning simulations on realistic, three-dimensional polycrystals.